What causes line to be 'retrained', how can I avoid it?

[#1]

I plan on doing some major adjustments to my network. I am on PN Unlimited, ADSL2+ over POTS, not fibre or anything fancy. Oh, other than a /29 subnet of IP addresses.
My concern is that my connection will get messed up. It seems almost every time I make any changes, or (more often) BT do any work at the local exchange, my connection is severely slowed down for a couple of weeks. It rarely goes back to normal (almost the maximum 20+Mbps speed) without me raising tickets and making many phone calls, and repeatedly having to go through the 'it isn't my fault' fault-finding when it's always BT that's the problem. Thus I am afraid to even sneeze near the modem.
So, how can I avoid this?
One of the main changes after re-cabling is to use either a Cisco ASA5505 after putting my modem in bridge mode, or just use a Cisco 1801 with built-in ADSL. I'll probably go with the 1801 because I want to use the ASA for learning Cisco certification stuff on.
Is the line training on a physical connection basis? In other words, if I have the phone line physically connected, could I then play with the settings on my side without causing the line speed to be messed up? Or, does the line training rely on a properly configured logical connection?
I'm guessing it's the latter, but hoping I'm wrong.
Just getting a connection to PN from a Cisco box might take some fiddling, never mind setting up the firewall and my side of the routing. I've never done it before with Cisco kit.
Rick.

[#2]

The critical thing is whether the router maintains sync with the exchange. If the exchange sees multiple drops of sync in a short period the DLM will intervene and cause the issues you've seen in the past. Dropping PPP only will not cause any issues. From what you've said you may be able to do some of the changes without rebooting the router. As far as possible you should totally disconnect the router from the phone while you mess about with internal networking which might require a loss of sync/reboot.
When you are going to lose sync do a disconnect via the router interface first; an orderly disconnect is less likely to be seen by the DLM as a problem.

[#3]

unplug the router from the phone line before you start if your going to be restarting it more than once, make sure to log into the router first though and close the connection (click disconnect)

this *should* stop the dlm from thinking the line lost sync and taking measures to try and get it back, then in theory at least once your finished with the network changes you can plug it back into the phone line and all will be well,
it might still have some loss but it shouldn't be anything to high 

[#4]

Thanks for the suggestion folks, they make sense to me. I'll certainly try them out and hope for the best.